Differential approximation fitting multi-path Beidou data fusion method
By employing a multi-channel BeiDou data fusion method based on differential approximation fitting, the universality and robustness issues of BeiDou satellite positioning technology are resolved, achieving high-precision and low-cost positioning results. This method is applicable to fields such as transportation, agriculture, forestry and fisheries, hydrological monitoring, weather forecasting, power dispatching, and disaster prevention and mitigation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-18
- Publication Date
- 2026-04-03
AI Technical Summary
Existing BeiDou satellite positioning technology suffers from poor universality, high cost, and poor robustness, making it difficult to achieve high-precision and high-reliability positioning, especially in complex environments.
A multi-source BeiDou data fusion method using differential approximation fitting is adopted. Through multi-source data preprocessing, initial reference benchmark construction, dynamic weight calculation of robust estimation theory, refined benchmark construction, and spatial surface fitting, the system error is successively approximated and corrected to achieve high-precision fusion positioning.
It improves positioning accuracy and stability, can automatically identify and isolate gross errors in complex environments, reduces dependence on external reference stations and data links, is suitable for various dynamic platforms, and has high versatility.
Smart Images
Figure CN121784789A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of satellite navigation and positioning technology, specifically relating to a multi-path BeiDou data fusion method using differential approximation fitting. Background Technology
[0002] The BeiDou Navigation Satellite System is a crucial space infrastructure independently constructed, operated, open, compatible, and serving the world by my country. It is widely used in transportation, agriculture, forestry, fisheries, hydrological monitoring, weather forecasting, power dispatching, disaster prevention and mitigation, and public safety, generating significant economic and social benefits. Various fields have a demand for high-precision, high-reliability location information. The location information received by a single BeiDou receiver is affected by a combination of interference factors, including satellite orbital errors, ephemeris clock errors, ionospheric / tropospheric delays, multipath effects, and internal receiver noise. This can result in deviations at the decimeter or even meter level, making it difficult to meet the high-end applications requiring millimeter-level deformation monitoring for geological disasters, centimeter-level path planning for unmanned vehicles, and sub-meter-level precision agriculture operations in terms of positioning accuracy and stability.
[0003] To improve positioning performance, the industry currently mainly uses real-time dynamic differential (RTK) positioning technology and data fusion technology based on filtering algorithms. However, these technologies have problems such as poor universality, high cost, and poor robustness, as detailed below.
[0004] (1) High cost and high dependence on external factors. Mainstream RTK technology relies on base stations with known coordinates, which is costly. The mobile station needs to be able to connect to the base station information at any time. The communication link is easily affected by weather conditions, terrain obstruction, electromagnetic interference and signal blind spots, resulting in low positioning accuracy.
[0005] (2) It is highly dependent on dynamic models and has weak environmental adaptability. Data fusion methods based on Kalman filtering or its derivative algorithms require prior establishment of a system dynamic model and obtaining accurate noise statistical characteristics. In complex dynamic environments, the filtering is prone to divergence due to low model matching, resulting in weak adaptability.
[0006] (3) Insufficient ability to suppress gross errors and simple fusion strategy. Direct fusion methods such as arithmetic mean and empirical weighted average are used to directly fusion multiple observation data. There is a lack of effective ability to identify and suppress gross errors. During the fusion process, gross errors are easily introduced into the fused data, reducing the final fusion accuracy.
[0007] Based on the above issues, a new data fusion technology is needed in the field of high-precision positioning, which has the characteristics of autonomy, high robustness, high precision, and model-free operation, to provide a solution for low-cost and highly reliable precision positioning. Summary of the Invention
[0008] (a) Technical problems to be solved The technical problem to be solved by this invention is how to provide a multi-path BeiDou data fusion method using differential approximation fitting, so as to solve the problems of poor universality, high cost and poor robustness of existing technologies.
[0009] (II) Technical Solution To address the aforementioned technical problems, this invention proposes a multi-path BeiDou data fusion method using differential approximation fitting, which includes the following steps: Step 1: Multi-source data preprocessing and spatiotemporal alignment The system's input receives raw positioning data from three or more independent BeiDou receivers or observation units for the same target, including latitude, longitude, elevation, and timestamp information from each observation station, and performs data preprocessing and spatiotemporal alignment. Step 2: Initial Reference Baseline Construction and First Round of Difference Calculation Establish a stable initial fusion center based on the original observations and calculate the first round of difference vectors; Step 3: Dynamic weight calculation based on robust estimation theory Statistical analysis is performed on the first round of difference vector sequences to obtain the overall dispersion. Then, a robust weight function is used to obtain the initial robust weights for each observation source. The larger the residual of the observation value, the smaller the initial weight. Step 4: Refining the baseline construction, fitting the spatial surface, and correcting the observed values. Identify and correct spatial correlation errors in the observation field; obtain a center point of a weighted average based on the robust weights obtained in the previous step, which serves as the "refinement benchmark"; establish a local Cartesian coordinate system with the refinement benchmark as the origin; project all observation points onto this coordinate system and calculate the second round of difference vectors; treat the two-dimensional latitude and longitude residuals as discrete sampling points on this local plane and use a low-order polynomial surface fitting; calculate the systematic error estimate for each observation point based on this surface, and subtract it from the original observation values of each observation point to correct the observation values and further improve the quality of the observation data; Step 5: Optimal Fusion Solution and Result Output The corrected high-quality data is fused and calculated; based on the corrected observations and refined benchmark, the new corrected residuals are calculated, and the final weight values are calculated using robust weight functions; the corrected observations and their corresponding final weights are averaged to obtain the high-quality fused location points.
[0010] (III) Beneficial Effects This invention proposes a multi-channel BeiDou data fusion method using differential approximation fitting. Compared to previous methods, this invention identifies and corrects spatially correlated systematic errors through the synergistic effect of "internal differential analysis, robust weighting, surface fitting, and successive approximation," thereby improving the accuracy of the final fusion result. The introduced robust weight function can automatically and in real-time identify and isolate anomalous observations with gross errors, enhancing the system's survivability in complex electromagnetic and harsh physical environments. It eliminates dependence on external reference stations and data links, lowering the barrier to entry for high-precision positioning technology. This invention focuses only on the spatial geometric relationships of multiple observation data at this specific moment, enabling seamless application to various dynamic platforms without requiring the redesign and parameter tuning of complex dynamic models for each specific application, thus exhibiting extremely high versatility. Attached Figure Description
[0011] Figure 1 This is the overall architecture of the present invention; Figure 2 This is a flowchart of step one of the present invention: multi-source data preprocessing and spatiotemporal alignment; Figure 3 This is a flowchart of step two of the present invention: initial reference benchmark construction and first round of difference calculation; Figure 4 This is a flowchart of step three of the present invention: dynamic weight calculation based on robust estimation theory; Figure 5 This is a flowchart of step four of the present invention: refinement of benchmark construction, spatial surface fitting, and observation correction. Figure 6 This is a flowchart of step five of the present invention: optimal fusion solution and result output. Detailed Implementation
[0012] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.
[0013] This invention relates to the field of satellite navigation and positioning technology, and in particular to a fusion processing technology based on multi-source BeiDou Navigation Satellite System (BDS) observation data. Specifically, it is a multi-source BeiDou data fusion method that utilizes differential approximation and surface fitting concepts to improve positioning accuracy and stability.
[0014] The fundamental objective of this invention is to overcome the shortcomings of existing technologies and provide a novel differential approximation fitting and fusion technique. This invention aims to specifically solve the following three key technical problems: (1) Self-improvement of accuracy. Without relying on external RTK base stations or network RTK services, a high-precision positioning result with a much higher accuracy than that of a single receiver, or even approaching the differential level, is generated endogenously by fusing data from multiple BeiDou receivers with ordinary accuracy.
[0015] (2) Gross error identification and suppression. In the case of multi-channel parallel observation, an adaptive and robust weighting method is designed to automatically and quickly identify gross errors caused by instantaneous interference and significantly reduce the proportion of such errors in the fusion results. Even when the reliability of the detection source is unstable, the fusion system can still output accurate results.
[0016] (3) Model dependence and environmental adaptability issues. To address the problem that traditional Kalman filtering, extended Kalman filtering and other methods rely on accurate system dynamics models and noise statistics, a data-driven data fusion modeling method based on the spatial geometric relationship of observations is proposed, which can adapt to various dynamic changes and complex environments.
[0017] To achieve the aforementioned objectives, this invention proposes a multi-channel BeiDou data fusion technique using differential approximation fitting. The core of this technique lies in treating multi-channel observation data as a dynamic "observation field," obtaining the relative residuals using a method based on an internal reference benchmark, then approximating and correcting systematic spatial errors using spatial surface fitting, and finally deriving the optimal fusion solution using a robust weighted approach. The entire scheme is a successive approximation, self-calibrating data processing method, comprising the following five steps: Step 1: Multi-source data preprocessing and spatiotemporal alignment This preparatory work addresses the benchmark discrepancies caused by different data sources, preparing for subsequent multi-source data fusion processing. The system's input receives raw positioning data from three or more (N≥3) independent BeiDou receivers or observation units targeting the same target. This data primarily includes latitude, longitude, elevation, and timestamps from each observation station. The data processing first involves time alignment of the multi-source data. Based on a unified system clock reference, the timestamps of all input data are uniformly corrected. Information that does not conform to the standard time series is corrected to the same time series using linear interpolation. Next, spatial alignment is performed. Existing mature spatial coordinate transformation algorithms are used to align all input data to a unified standard spatial coordinate system, ensuring all observations are under the same spatial reference, laying the foundation for subsequent differential calculations.
[0018] Step 2: Initial Reference Baseline Construction and First Round of Difference Calculation A stable initial fusion center is established based on the original observations. At any fusion time point, the arithmetic mean method is used to average the coordinates of all N preprocessed valid observation points to calculate an initial reference benchmark point, which represents the "geometric center" of the spatial domain formed by all original observation points at a certain time point. Subtracting this initial benchmark point from the coordinates of each point yields a first-round difference vector, quantifying the deviation of each observation value from the true coordinates, including all unknown error terms that need to be processed subsequently, such as random errors, systematic errors, and gross errors, providing basic data for subsequent weight calculation and error fitting.
[0019] Step 3: Dynamic weight calculation based on robust estimation theory Statistical analysis is performed on the first round of difference vector sequences to obtain the overall dispersion. Then, a robust weight function is used to obtain the initial robust weight for each observation source. The larger the residual of the observation value, the smaller the initial weight, thereby minimizing the impact of gross errors, ensuring the stability of numerical calculation, and reducing the sensitivity of the fusion process to outlier data.
[0020] Step 4: Refining the baseline construction, spatial surface fitting, and observation correction Identify and correct spatial correlation errors in the observation field. Based on the robust weights obtained in the previous step, obtain the center point of a weighted average as a "refinement benchmark." Establish a local Cartesian coordinate system with the refinement benchmark as the origin, project all observation points onto this coordinate system, and calculate the second round of difference vectors. Treat the two-dimensional latitude and longitude residuals as discrete sampling points on this local plane, and use a low-order polynomial surface fitting method. The fitting process employs weighted least squares to improve robustness. Based on this surface, calculate the systematic error estimate for each observation point, subtract it from the original observation values for each point, correct the observation values, and further improve the quality of the observation data.
[0021] Step 5: Optimal Fusion Solution and Result Output The corrected high-quality data is fused and calculated. Based on the corrected observations and refined baseline, the new corrected residuals are calculated, and the final weight values are calculated using a robust weight function. The corrected observations and their corresponding final weights are then averaged to obtain high-precision, high-stability, and high-reliability fused positioning points.
[0022] Example 1: This invention proposes a multi-channel BeiDou data fusion technique using differential approximation fitting. It abandons the single concept of "absolute coordinates" and treats multi-channel observation data as a dynamic "observation field." By constructing an internal reference benchmark, calculating relative residuals, fitting the error space surface, and successively approximating and correcting, the optimal positioning estimate is extracted from the internal structure of the data field.
[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0024] Step 1: Multi-source data preprocessing and spatiotemporal alignment (1) Data input: The system interface continuously receives data from... The data stream from the BeiDou receiver. Each data stream should include at least: UTC timestamp, longitude, latitude, elevation, and information such as the positioning solution mode used to assess data quality and the number of satellites used.
[0025] (2) Time Alignment: The system maintains an internal high-precision clock as a reference. Upon receiving data from each channel, the difference between its timestamp and the reference time is compared. For data that is not strictly real-time or has a fixed delay, compensation must be provided in the software. For asynchronous data, linear interpolation is used. Assuming in and The coordinates of a certain receiver are received at all times. and It needs to be in The value at time ( If so, use the formula.
[0026] Interpolation is performed to map all data to a series of fusion time points with equal time intervals.
[0027] (3) Spatial alignment: If the coordinate system of the input coordinates is different from the target coordinate system, coordinate transformation is required. For example, using the Bursa seven-parameter model, the coordinate system is transformed from CGCS2000 to WGS-84 through standardized spatial matrix operations. The coordinate system transformation parameters are stored in a dedicated configuration file. During the transformation process, the transformation function is called to calculate the coordinate values under the unified coordinate system for each obtained coordinate point.
[0028] Step 2: Initial Reference Baseline Construction and First Round of Difference Calculation S21, Baseline Construction: Assume that at the current fusion time... The effective observation point, the first The WGS-84 coordinates of the points are as follows:
[0029] in , Represents longitude. Represents latitude, Represents elevation. Initial reference point. The calculation formula is:
[0030] Right now:
[0031] This point is an unbiased statistical center.
[0032] S22. Difference Calculation: Calculate the difference between each point and... The difference is used to obtain the first round difference vector. :
[0033] These vectors form the original residual sequence for subsequent analysis.
[0034] Step 3: Dynamic weight calculation based on robust estimation theory S31. Residual Analysis: Calculate the Euclidean norm of the first-round difference vector in the horizontal direction (longitude, latitude) for a point. Its norm
[0035] This comprehensively reflects the degree of deviation of the point from the horizontal plane. Simultaneously, it can calculate all... The "root mean square error (RMSE)" is used to assess the overall horizontal dispersion of the observation field at this moment:
[0036] S32. Assigning Robust Weights: The following function is used to calculate the weights for the first round. :
[0037] in, It is a sensitivity factor greater than 0. The larger the value, the more severe the penalty for large residuals, and the faster the weight decays. In practical applications, The initial value can be set to 1.0. This weight function guarantees that even if... It's very big. It will not be zero, thus avoiding numerical issues and achieving strong suppression of gross errors.
[0038] Step 4: Refining the baseline construction, spatial surface fitting, and observation correction S41. Refining the benchmark construction: Using the weights obtained in step three. Calculate the weighted average center :
[0039] The component form is:
[0040] This point represents an optimization of the initial baseline.
[0041] S42. Establishment of Local Coordinate System and Secondary Difference: Establish a "local tangent plane coordinate system" with the origin as the origin, and use a standard coordinate transformation process to transform the points in the global coordinate system. Convert to local coordinates Simultaneously, the second round difference vector is calculated.
[0042] S43. Spatial Surface Fitting: Fitting Latitude and Longitude Residuals Consider as a local plane The function is fitted using a quadratic surface model.
[0043] Longitude residual The calculation model is as follows:
[0044] Latitude residual The calculation model is as follows:
[0045] The fitting was performed using the weighted least squares method, with the weight parameters calculated in step three. By solving the system of equations
[0046] in,
[0047] And by minimizing the weighted sum of squared residuals, the coefficient vector of the computational model is obtained. and .
[0048] S44. Observation Correction: For each observation point Set its local coordinates Substituting the fitted surface equation, we calculate its estimated systematic error:
[0049] Then the coordinates of the observation point After correction, the coordinates of the purified observation point are obtained:
[0050] Elevation One-dimensional curve fitting or independent correction using robust weighted averaging can be used to obtain the result. .
[0051] The observed values were obtained after correction. .
[0052] Step 5: Optimal Fusion Solution and Result Output S51. Final Weight Calculation: Calculate the corrected observations. Compared with the refinement benchmark residuals:
[0053] Similarly, calculate its level norm. :
[0054] The final weights are calculated using the same robust weight function as in step three. :
[0055]
[0056] At this point, the previous sensitivity factors can be reused. It can also be fine-tuned based on the quality of the corrected data.
[0057] S52. Weighted Fusion and Output: The final high-precision fusion positioning result Calculated using the following formula:
[0058] Will The coordinate results of this fusion cycle are output to support upper-layer applications such as navigation, positioning, and monitoring.
[0059] Beneficial effects This invention proposes a multi-channel BeiDou data fusion technique using differential approximation fitting. Compared to previous methods, this invention identifies and corrects spatially correlated systematic errors through the synergistic effect of "internal differential analysis, robust weighting, surface fitting, and successive approximation," thereby improving the accuracy of the final fusion result. The introduced robust weight function can automatically and in real-time identify and isolate anomalous observations with gross errors, enhancing the system's survivability in complex electromagnetic and harsh physical environments. It eliminates dependence on external reference stations and data links, lowering the barrier to entry for high-precision positioning technology. This invention focuses only on the spatial geometric relationships of multiple observation data at this specific moment, enabling seamless application to various dynamic platforms without requiring the redesign and parameter tuning of complex dynamic models for each specific application, thus exhibiting extremely high versatility.
[0060] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A multi-channel BeiDou data fusion method using differential approximation fitting, characterized in that, The method includes the following steps: Step 1: Multi-source data preprocessing and spatiotemporal alignment The system's input receives raw positioning data from three or more independent BeiDou receivers or observation units for the same target, including latitude, longitude, elevation, and timestamp information from each observation station, and performs data preprocessing and spatiotemporal alignment. Step 2: Initial Reference Baseline Construction and First Round of Difference Calculation Establish a stable initial fusion center based on the original observations and calculate the first round of difference vectors; Step 3: Dynamic weight calculation based on robust estimation theory Statistical analysis is performed on the first round of difference vector sequences to obtain the overall dispersion. Then, a robust weight function is used to obtain the initial robust weights for each observation source. The larger the residual of the observation value, the smaller the initial weight. Step 4: Refining the baseline construction, fitting the spatial surface, and correcting the observed values. Identify and correct spatial correlation errors in the observation field; obtain a center point of a weighted average based on the robust weights obtained in the previous step, which serves as the "refinement benchmark"; establish a local Cartesian coordinate system with the refinement benchmark as the origin; project all observation points onto this coordinate system and calculate the second round of difference vectors; treat the two-dimensional latitude and longitude residuals as discrete sampling points on this local plane and use low-order polynomial surface fitting; calculate the systematic error estimate for each observation point based on this surface, and subtract it from the original observation values of each observation point to correct the observation values and further improve the quality of the observation data; Step 5: Optimal Fusion Solution and Result Output The corrected high-quality data is fused and calculated; based on the corrected observations and refined benchmark, the corrected new residuals are calculated, and the final weight values are calculated using robust weight functions; The corrected observations are averaged with their corresponding final weights to obtain high-quality fused localization points.
2. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 1, characterized in that, In step one, during data processing, the time alignment of multi-source data is first completed. Based on a unified system clock reference, the timestamps of all input data are uniformly corrected. Information that does not conform to the standard time series can be corrected to the same time series using linear interpolation. Then, the spatial alignment of the data is performed. A spatial coordinate transformation algorithm is used to align all input data to a unified standard spatial coordinate system, ensuring that all observations are under the same spatial reference, thus laying the foundation for subsequent difference calculations.
3. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 1, characterized in that, Step two includes: at any fusion time point, using the arithmetic mean method, averaging the coordinates of all N preprocessed valid observation points to calculate an initial reference benchmark point, which is used to characterize the "geometric center" of the spatial domain formed by all original observation points at a certain time point; subtracting this initial benchmark point from the coordinates of each point to obtain a first-round difference vector, quantifying the degree of deviation of each observation value from the true coordinates, including random error, systematic error and gross error, to provide basic data for subsequent weight calculation and error fitting.
4. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 1, characterized in that, In step four, the fitting process uses weighted least squares to improve robustness.
5. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 1, characterized in that, Step one includes: (1) Data input: The system interface continuously receives data from... The data stream of the Beidou receiver; each data stream should include at least: UTC timestamp, longitude, latitude, elevation, and positioning solution mode and satellite number information used to assess data quality; (2) Time alignment: The system maintains an internal high-precision clock as a reference; after receiving data from each channel, the difference between its timestamp and the reference time is compared; for data that is not strictly real-time or has a fixed delay, compensation needs to be made in the software; for asynchronous data, linear interpolation is used. Suppose that the coordinates of a receiver are received at times t1 and t2. and It needs to be in If the value at time t1 < t < t2, then use the formula Interpolation is performed to map all data to a series of fusion time points with equal time intervals; (3) Spatial alignment: If the coordinate system of the input coordinates is different from the target coordinate system, coordinate transformation is required. Through standardized spatial matrix operations, the coordinate system is transformed from CGCS2000 coordinate system to WGS-84 coordinate system. The coordinate system transformation parameters are stored in a special configuration file. During the transformation process, the transformation function is called to calculate the coordinate values under the unified coordinate system for each obtained coordinate point.
6. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 1, characterized in that, Step two includes: S21, Baseline Construction: Assume that at the current fusion time... The effective observation point, the first The WGS-84 coordinates of the points are as follows: in , Represents longitude. Represents latitude, Represents elevation; initial reference benchmark. The calculation formula is: Right now: This point is an unbiased statistical center; S22. Difference Calculation: Calculate the difference between each point and... The difference is used to obtain the first round difference vector. : These vectors form the original residual sequence for subsequent analysis.
7. The multi-path BeiDou data fusion method using differential approximation fitting as described in claim 6, characterized in that, Step three includes: S31. Residual Analysis: Calculate the Euclidean norm of the first-round difference vector in the horizontal direction for a point. Its norm It comprehensively reflects the degree of deviation of the point from the horizontal plane; at the same time, it can calculate all The "root mean square error (RMSE)" is used to assess the overall horizontal dispersion of the observation field at this moment: S32. Assigning Robust Weights: The following function is used to calculate the weights for the first round. : in, It is a sensitivity factor greater than 0; The larger the value, the more severe the penalty for large residuals, and the faster the weight decays; this weight function ensures that even if... It's very big. It will not be zero, thus avoiding numerical issues and achieving strong suppression of gross errors.
8. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 7, characterized in that, The initial value is set to 1.
0.
9. The multi-channel BeiDou data fusion method using differential approximation fitting as described in claim 7, characterized in that, Step four includes: S41. Refining the benchmark construction: Using the weights obtained in step three. Calculate the weighted average center : The component form is: This point is an optimization of the initial baseline; S42. Establishment of Local Coordinate System and Secondary Difference: Establish a "local tangent plane coordinate system" with the origin as the origin, and use a standard coordinate transformation process to transform the points in the global coordinate system. Convert to local coordinates Simultaneously, calculate the second round difference vector. S43. Spatial Surface Fitting: Fitting Latitude and Longitude Residuals Consider as a local plane The function on the surface is fitted using a quadratic surface model; Longitude residual The calculation model is as follows: Latitude residual The calculation model is as follows: The fitting was performed using the weighted least squares method, with the weight parameters calculated in step three. By solving the system of equations in, And by minimizing the weighted sum of squared residuals, the coefficient vector of the computational model is obtained. and ; S44. Observation Correction: For each observation point Set its local coordinates Substituting the fitted surface equation, we calculate its estimated systematic error: Then the coordinates of the observation point After correction, the coordinates of the purified observation point are obtained: Elevation One-dimensional curve fitting or independent correction using robust weighted averaging can be used to obtain the result. ; The observed values were obtained after correction. .
10. The multi-path BeiDou data fusion method using differential approximation fitting as described in claim 9, characterized in that, Step five includes: S51. Final Weight Calculation: Calculate the corrected observations. Compared with the refinement benchmark residuals: Similarly, calculate its level norm. : The final weights are calculated using the same robust weight function as in step three. : S52. Weighted Fusion and Output: The final high-precision fusion positioning result Calculated using the following formula: Will The coordinate results for this fusion cycle will be output.